How light can ALP dark matter be?

We assume axion-like particles (ALPs) emerging as pseudo-Goldstone bosons from a global U(1) symmetry to provide the dark matter in the universe and derive various lower bounds on the ALP mass. Focusing first on post-inflationary symmetry breaking, we revisit bounds from isocurvature perturbations taking into account that, as suggested by recent simulations, axion radiation by cosmic strings during the scaling regime provides the dominant production mechanism of dark matter. Furthermore, we point out that the upper bound on the energy scale of inflation from the non-observation of CMB tensor modes provides a complementary lower bound on the ALP mass. We contrast the post- and pre-inflationary symmetry breaking cases and present allowed regions in the plane of ALP mass and energy scale of inflation. Combining isocurvature and CMB tensor mode bounds with constraints from black hole superradiance, we find bounds of order $m_a > 10^{-17}$ eV to apply in most cases. However, significantly stronger bounds may apply in specific scenarios.